State Estimation Problems in Heat Transfer

Orlande, Helcio R. B.; Colaço, Marcelo J.; Dulikravich, George S.; Vianna, Flavio L. V.; Silva, Wellington da; Fonseca, Henrique Massard da; Fudym, Olivier

doi:10.1615/int.j.uncertaintyquantification.2012003582

Cited by 28 publications

(33 citation statements)

References 22 publications

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“…. ‚ kg given by the observation model (8.b) (Kalman, 1960;Sorenson, 1970;Maybeck, 1979;Liu and Chen, 1998;Carpenter et al, 1999;Doucet et al, 2000Doucet et al, , 2001Arulampalam et al, 2001;Winkler, 2003;Andrieu et al, 2004a,b;Kaipio and Somersalo, 2004;Ristic et al, 2004;Kaipio et al, 2005;Del Moral et al, 2006Welch and Bishop, 2006;Johansen and Doucet, 2008;Orlande et al, 2012). The evolution-observation model given by Equations (8.a,b) is based on the following assumptions (Maybeck, 1979;Winkler, 2003;Kaipio and Somersalo, 2004):…”

Section: State Estimation Problem and Methods Of Solutionmentioning

confidence: 99%

“…By assuming that p(x 0 jz 0 ) = p(x 0 ) is available, the posterior probability densityp(x k jz 1:k ) is then obtained with Bayesian filters in two steps: prediction and update (Kalman, 1960;Sorenson, 1970;Maybeck, 1979;Liu and Chen, 1998;Carpenter et al, 1999;Doucet et al, 2000Doucet et al, , 2001Arulampalam et al, 2001;Liu and West, 2001;Winkler, 2003;Andrieu et al, 2004a,b;Kaipio and Somersalo, 2004;Ristic et al, 2004;Kaipio et al, 2005;Del Moral et al, 2006Welch and Bishop, 2006;Johansen and Doucet, 2008;Orlande et al, 2012). In the prediction step, the particles are advanced in time with the state evolution model, providing a prior distribution for the state variables.…”

Section: State Estimation Problem and Methods Of Solutionmentioning

confidence: 99%

“…Sequential Monte Carlo methods, usually denoted as particle filters, have also been developed in order to represent the posterior density in terms of random samples and associated weights. Particle filters do not require the restrictive hypotheses of the Kalman filter; that is, they can be applied to nonlinear models with non-Gaussian errors (Liu and Chen, 1998;Carpenter et al, 1999;Doucet et al, 2000Doucet et al, , 2001Arulampalam et al, 2001;Andrieu et al, 2004a,b;Kaipio and Somersalo, 2004;Ristic et al, 2004;Kaipio et al, 2005;Del Moral et al, 2006Johansen and Doucet, 2008;Orlande et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Resampling deals with the elimination of particles originally with low weights and the replication of particles with high weights. Resampling can be performed if the number of effective particles (particles with large weights) falls below a certain threshold number (Kalman, 1960;Sorenson, 1970;Maybeck, 1979;Liu and Chen, 1998;Carpenter et al, 1999;Doucet et al, 2000Doucet et al, , 2001Arulampalam et al, 2001;Liu and West, 2001;Winkler, 2003;Andrieu et al, 2004a,b;Kaipio and Somersalo, 2004;Ristic et al, 2004;Kaipio et al, 2005;Del Moral et al, 2006Welch and Bishop, 2006;Johansen and Doucet, 2008;Orlande et al, 2012). Alternatively, resampling can also be applied indistinctively at every instant t k , as in the sampling importance resampling (SIR) algorithm described in (Arulampalam et al, 2001;Ristic et al, 2004).…”

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confidence: 99%

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Estimation of Tumor Size Evolution Using Particle Filters

Costa

Orlande

Velho

et al. 2015

Journal of Computational Biology

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Cancer is characterized by the uncontrolled growth of cells with the ability of invading local organs and/or tissues and of spreading to other sites. Several kinds of mathematical models have been proposed in the literature, involving different levels of refinement, for the evolution of tumors and their interactions with chemotherapy drugs. In this article, we present the solution of a state estimation problem for tumor size evolution. A system of nonlinear ordinary differential equations is used as the state evolution model, which involves as state variables the numbers of tumor, normal and angiogenic cells, as well as the masses of the chemotherapy and anti-angiogenic drugs in the body. Measurements of the numbers of tumor and normal cells are considered available for the inverse analysis. Parameters appearing in the formulation of the state evolution model are treated as Gaussian random variables and their uncertainties are taken into account in the estimation of the state variables, by using an algorithm based on the auxiliary sampling importance resampling particle filter. Test cases are examined in the article dealing with a chemotherapy protocol for pancreatic cancer.

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Section: State Estimation Problem and Methods Of Solutionmentioning

confidence: 99%

Section: State Estimation Problem and Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Estimation of Tumor Size Evolution Using Particle Filters

Costa

Orlande

Velho

et al. 2015

Journal of Computational Biology

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“…Particle filters approximate the sequences of posterior probability distributions of state variables or unknown parameters in state-space models. For example, in Orlande et al [24], an auxiliary particle-filter algorithm was applied to estimate the unsteady temperature field of the fluid inside multilayered oil pipelines during shutdown periods. Moreover, these authors also estimated a position-dependent transient heat source in a plate, although in this case, the exact solution to the problem was obtained using a Kalman filter, due to the linear Gaussian temperature-evolution model.…”

Section: Standards and Literature Reviewmentioning

confidence: 99%

A Particle-Filtering Approach for Real-Time Estimation of Thermal Conductivity and Temperature Tracking in Homogeneous Masses

Martín-Fernández

Lanzarone

2015

Numerical Heat Transfer, Part B: Fundamentals

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Knowledge of the thermal conductivity is a key factor for several applications, which benefits from easy and cheap estimation procedures. We consider an existing experimental layout, and we propose a Rao-Blackwellized particle filter that jointly approximates the posterior distribution of the temperatures and analytically estimates the unknown thermal conductivity of a homogeneous mass. Its main advantage is the sequential estimation of the conductivity. In contrast, in other approaches, all of the temperatures need to be stored before processing the data. The results obtained with a polymethylmethacrylate specimen provide good estimates and demonstrate the real-time applicability of the approach.

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Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia

Nagesetti

Dulikravich

Orlande

et al. 2021

Numer Methods Biomed Eng

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Drug delivery to tumors suffers from poor solubility, specificity, diffusion through the tumor micro‐environment and nonoptimal interactions with components of the extracellular matrix and cell surface receptors. Nanoparticles and drug–polymer complexes address many of these problems. However, large size exasperates the problem of slow diffusion through the tumor. Three‐dimensional tumor spheroids are good models to evaluate approaches to mitigate these difficulties and aid in design strategies to improve the delivery of drugs to treat cancer effectively. Diffusion of drug carriers is highly dependent on cell uptake rate parameters (association/dissociation) and temperature. Hyperthermia increases molecular transport and is known to act synergistically with chemotherapy to improve treatment. This study presents a new inverse estimation approach based on Bayesian probability for estimating nanoparticle cell uptake rates from experiments. The parameters were combined with a finite element computational model of nanoparticle transport under hyperthermia conditions to explore its effect on tumor porosity, diffusion and particle binding (association and dissociation) at cell surfaces. Carboxy‐PEG‐silane (cPEGSi) nanoparticles showed higher cell uptake compared to methoxy‐PEG‐silane (mPEGSi) nanoparticles. Simulations were consistent with experimental results from Skov‐3 ovarian cancer spheroids. Amorphous silica (cPEGSi) nanoparticles (58 nm) concentrated at the periphery of the tumor spheroids at 37°C but mild hyperthermia (43°C) increased nanoparticle penetration. Thus, hyperthermia may enhance cancer treatment by improving blood delivery to tumors, enhancing extravasation and penetration into tumors, trigger release of drug from the carrier at the tumor site and possibly lead to synergistic anti‐cancer activity with the drug.

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State Estimation Problems in Heat Transfer

Cited by 28 publications

References 22 publications

Estimation of Tumor Size Evolution Using Particle Filters

Estimation of Tumor Size Evolution Using Particle Filters

A Particle-Filtering Approach for Real-Time Estimation of Thermal Conductivity and Temperature Tracking in Homogeneous Masses

Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia

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